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ARCHIMEDES’ PRINCIPLE
Purpose: To verify Archimedes’ Principle. To apply Archimedes’ Principle to the experimental
determination of densities and specific gravities of solids and liquids. Apparatus: Triple beam balance; vernier calipers; one metal cylinder with copper wire suspension; one
hollow block; tap water; liquid X.
Theory: Archimedes’ Principle states that any object completely or partially submerged in a fluid is
buoyed up by a force with magnitude equal to the weight of the weight of the fluid displaced by the
object:
B = ρfluid Vfluid g ,
where ρfluid is the density of the fluid and Vfluid is the volume of the displaced fluid. In this lab, all the
forces and weights are measured in the unit of grams using the triple beam balance, then the above
equation becomes:
B = ρfluid Vfluid .
Figure 1
When measuring the weight of an object completely submerged in a fluid, as shown in Fig. 1, the volume
of the displaced fluid is equal to the volume of the object, and the reading on the balance (Win-fluid), the
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buoyant force, and its weight in air (Win-air) should satisfy the following equation:
B = Win-air - Win-fluid = ρfluid Vobject .
Thus, the volume of the object can be determined as:
Vobject = (Win-air - Win-fluid)/ ρfluid ,
and the density and the specific gravity of the object are, respectively:
ρobject = Win-air / Vobject = ρfluid Win-air / (Win-air - Win-fluid),
s.g. = ρobject / ρwater .
Procedures:
1. Measure the diameter (D) and height (h) of the cylinder with the vernier caliper.
2. Suspend the metal cylinder by the fine wire from the hook of the balance, over the scale pan. (Do
not remove the pan.) Weigh the cylinder in air.
3. Place a beaker of water on the adjustable circular platform over the scale pan, and immerse the
cylinder completely. Weigh as before. Remove the beaker and carefully dry the cylinder.
4. Repeat Step 3, using liquid X instead of water.
5. Weigh the hollow block in air. Slip the lower end of the cylinder into the hole in the block. Weigh
the suspended block and cylinder in the liquid X, being sure that both block and cylinder are
completely submerged. Again remove the beaker and dry the block and cylinder.
Computation:
1. Verify Archimedes’ Principle: (a) Directly compute the volume of the cylinder using the
geometrical data measured by the caliper: Vcylinder = πD2h/4. Neglect the volume of the knob. (b)
Calculate the weight of the water displaced by the cylinder based on the cylinder’s volume and the
density of water. (c) Determine the buoyant force, which is the apparent loss of weight of the
cylinder when it is suspended in water. (d) Compare the results from (b) and (c). The agreement
between these two values shows how well you have verified Archimedes’ Principle. Enter these
results in Table 1.
2. Apply Archimedes’ Principle: Compute the densities and the specific gravities of the cylinder, the
liquid X, and the block. Compute the volume of the block. Show your works. Enter your results
in the Table 2. Indicate clearly the units for each quantity.
Questions:
1. By how many grams was the force on the bottom of the beaker increased when the cylinder was
immersed in water?
2. Show algebraically that for an object floating in water, the fraction of the volume under water is
equal to its specific gravity.
3. Where in this exercise is error introduced by neglecting the volume of the knob? Explain. What is
the magnitude of the error in your case?
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Diameter of cylinder
Height of cylinder
Volume of cylinder
Weight of water displaced by cylinder
Weight of cylinder in air
Weight of cylinder in water
Buoyant force (loss of weight of cylinder in water)
Percent error
Table 1: Verification of Archimedes' Principle. Items in bold indicate direct measurements. Weight of cylinder in air
Weight of cylinder in water
Weight of cylinder in liquid X
Weight of hollow block in air
Weight of block and cylinder in liquid X
Density of cylinder
Specific gravity of cylinder
Density of Liquid X
Specific gravity of Liquid X
Density of block
Specific gravity of block
Volume of block
Table 2: Application of Archimedes' Principle. Items in bold indicate direct measurements.